integer introduction. warm up write each decimal as a fraction. 1.) 1.8 = 2.) 15.25 = 3.).008 =...

Integer Introduction

Warm UpWrite each decimal as a fraction.

1.) 1.8 =

2.) 15.25 =

3.) .008 =

4.) .85 =

Objectives

Student Expectation: We will explore integers on a # line.

Product: I will explore integers on a # line

Vocabulary

oppositeintegerabsolute value

Create A Number Line

• Fold Sentence Strip in Half

• Place Zero (0) on sentence strip at fold

• Use a ruler and place marks at each inch.

• # the lines on each side of zero. Should go to 12 and -12.

Numbers on Number Line• On the LEFT side of zero, start with 1 and

the numbers get larger.

• Label the numbers on the LEFT side of zero with a negative sign (-); these are NEGATIVE NUMBERS and get smaller the farther you go from zero.

• The numbers on the RIGHT side of zero are POSITIVE NUMBERS and get larger the farther you go from zero.

The opposite of a number is the samedistance from 0 on a number line as theoriginal number, but on the other sideof 0. Zero is its own opposite.

1 2 3 4 5 • •

–5–4–3–2–1 0

–4 and 4 are opposites

–4 4

Negative integers Positive integers

0 is neither positivenor negative

The integers are the set of whole numbers and their opposites. By using integers, you can express elevations above, below, and at sea level. Sea level has an elevation of 0 feet.

The whole numbers are the counting numbers and zero: 0, 1, 2, 3, . . . .

Remember!

Graph the integer 7 and its opposite on a number line.

1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0

Graph the integer 5 and its opposite on a number line.

1 2 3 4 5 6 7 –7 –6–5 –4 –3–2–1 0

You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the left.

Compare the integers. Use < or >.

4 is farther to the right than -4, so 4 > -4.

1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0

4 -4>

The symbol < means “is less than,” and the symbol > means “is greater than.”

Remember!

Compare the integers. Use < or >.

-15 -9

-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Compare the integers. Use < or >.

1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0

6 -6

Compare the integers. Use < or >.

-4 -11

-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Use a number line to order the integers from least to greatest.

–3, 6, –5, 2, 0, –8

1 2 3 4 5 6 7 8 –8 –7–6 –5–4 –3 –2 –1 0

Use a number line to order the integers from least to greatest.

–5, 4, –3, 2, –1, –2

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

A number’s absolute value is its distance from 0 on a number line.

Since distance can never be negative, absolute values are never negative.

They are always positive or zero.

Use a number line to find each absolute value.

|8|

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

8 units

8 is 8 units from 0, so |8| = 8.

The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3.

Reading Math

Use a number line to find each absolute value.

|–12|

–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2

Use a number line to find each absolute value.

|3|

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

Use a number line to find the absolute value.

|–9|

–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2

Lesson Quiz: Part I

Compare. Use <, >, or =.

1. –32 32

2. 26 |–26|

3. –8 –12

4. Use a number line to order the integers –2, 3, –4, 5, and –1 from least to greatest.

1 2 3 4 5 –5–4 –3 –2–1 0

Lesson Quiz: Part II

Use a number line to find the absolute value.

5. -3

1 2 3 4 5 –5 –4 –3 –2 –1 0

3 units

Assignment

Practice 2-1